On constructions of surfaces using a geodesic in Lie group

Abstract

In this study, we investigate the problem how to characterize a surface family from a given common geodesic curve in a 3-dimensional Lie group G. We obtain a parametric representation of the surface as a linear combination of the Frenet frame in G. Also, we give the relation about developability along the common geodesic of the members of surface family. Finally, we illustrate some examples to verify this method.